If this is a "back to 100% original" refurb, this will be no help, but if it is solving a practical problem, I have three suggestions:
0. Use a cable gland instead: These are probably still easily available in imperial sizes, and will accommodate the thickness you need. If you don't want it visible, put it in with the strain relief part inside the box.
1. you can get various forms of grommet strip. This is U-section strip, either of rubber or nylon (mine is the latter), and sometimes with a serrated edge (to the panel side), to grip holes better. Use is pretty obvious - you work out the circumference of the hole, and subtract a tiny amount, then cut to length and push-fit. It comes in various sizes for different panel thicknesses.
2. Heatshrink and Hellermann sleeves: both of these do the same thing: thicken the insulation round the cable, both to add protection and some strain relief where it terminates.
Hellermann sleeves are rubber and extremely good, and go to pretty large diameters as they are used industrially, but you do need the fitting tongs. They have the huge advantage that you can often get them over connectors, so they can sometimes be retro-fitted to cables that are already terminated. They are reasonably heat-proof (they come from the days of valve electronic equipment, I think), but can perish, and being a natural material (I think), can be affected by chemicals. They come in a range of colours too, which is very handy.
Heatshrink, most people know. Bright colours are available, including white you can write on, and clear, and a range of sizes. There is a variant with a sealant inside, which oozes when heated so it really bonds to the cable, but it does make it very rigid.
In both cases you can stack them over themselves on the cable, making a thicker cable or tapering where it goes into a connector or through a grommet.
I think heatshrink is easier to use, but not as effective in providing strain relief as it's not anything like as flexible as Hellermann sleeves. But combining one or the other with grommet strip might get you what you need.
Finally, consider applying a countersink tool, gently, to the edges of the hole, to reduce the metal thickness slightly and take off any arris round the rim. This will help prevent chafing, and might even let you use a grommet intended for slightly thinner material.
By the way, use of cast metal boxes for industrial electrics and telecomms electronics is still common, as the metal can form a waterproof heatsink, and it's an aluminium alloy, doesn't corrode as easily as steel. As a consequence, glands and grommets are also available, although I'll admit 5/16" is thicker than usual.
HTH,
E.
